 Re: were inversion
First of all, notice that the example is ungrammatical for other reasons. It should be :
... what they know does not matter, were their knowledge (etc)
The inversion with "were" means that the speaker/wrter is tagging on a hypothetical statement to a factual statement, and you're right that there's a tension between the two. Is this a real situation or a hypothetical one? If this were written English, I'd expect consistency, though in spontaneous spoken communication there's often a mix of structures like this simply because by the time the speaker gets to the end of the sentence, they've lost track of what they said at the beginning.
However, the sentence also sounds odd because this use of inversion is fairly formal, while the rest of your sentence is neutral to informal. Where did you find it? I'd change it to :
a) If you want to express it as a "real" situation" :
(Formal) Their knowledge is immaterial, be it accurate or not.
or
(Informal) What they know doesn't matter, whether it's accurate or not.
b) If you want to express it as a hypothetical situation :
(Formal) Their knowledge would be immaterial, were it accurate or not.
or
(Informal) What they knew wouldn't matter, whether it was accurate or not. |